%A Pedro Paredes Gonzalez
%A Vassilios Theofilis
%A Daniel Rodr?guez ?lvarez
%A Juan Angel Tendero Ventanas
%T The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension
%X The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order ?nitedi?erence-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of e?ciency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity o?ered by the ?nite-di?erence scheme and, as expected, is shown to perform substantially more e?ciently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the ?ow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic ?ow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional ?ow composed of a counter-rotating pair of nonparallel Batchelor vortices.
%P 0-0
%B Proceedings of 6th Theoretical Fluid Mechanics Conference
%D 2011
%C EEUU
%I AIAA
%L upm13082